| An improved boundary element-free method （IBEFM） for two-dimensional potential problems |
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| 引用本文： | 任红萍,张武. An improved boundary element-free method （IBEFM） for two-dimensional potential problems[J]. 中国物理 B, 2009, 18(10): 4065-4073. DOI: 10.1088/1674-1056/18/10/002 |
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| 作者姓名： | 任红萍 张武 |
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| 作者单位： | School of Computer Engineering and Science, Shanghai University, Shanghai 200072, China |
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| 基金项目： | Project supported by the NationalNatural Science Foundation of China (Grant No 10871124), InnovationProgram of Shanghai Municipal Education Commission (Grant No 09ZZ99)and Shanghai Leading AcademicDiscipline Project (Grant No J50103). |
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| 摘 要： | The interpolating moving least-squares (IMLS) method is discussedfirst in this paper. And the formulae of the IMLS method obtained byLancaster are revised. Then on the basis of the boundaryelement-free method (BEFM), combining the boundary integral equation(BIE) method with the IMLS method, the improved boundaryelement-free method (IBEFM) for two-dimensional potential problemsis presented, and the corresponding formulae of the IBEFM areobtained. In the BEFM, boundary conditions are applied directly, butthe shape function in the MLS does not satisfy the property ofthe Kronecker δ function. This is a problem of the BEFM, andmust be solved theoretically. In the IMLS method, when the shape functionsatisfies the property of the Kronecker δ function, then theboundary conditions, in the meshless method based on the IMLSmethod, can be applied directly. Then the IBEFM, based on the IMLSmethod, is a direct meshless boundary integral equation method inwhich the basic unknown quantity is the real solution of the nodalvariables, and the boundary conditions can be applied directly andeasily, thus it gives a greater computational precision. Somenumerical examples are presented to demonstrate the method.
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| 关 键 词： | moving least-squares approximation interpolating moving least-squares method mesh-less method improved boundary element-free method potential problem |
| 收稿时间： | 2008-10-07 |
| 修稿时间： | 2009-02-01 |
An improved boundary element-free method (IBEFM) for two-dimensional potential problems |
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| Ren Hong-Ping and Zhang Wu. An improved boundary element-free method (IBEFM) for two-dimensional potential problems[J]. Chinese Physics B, 2009, 18(10): 4065-4073. DOI: 10.1088/1674-1056/18/10/002 |
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| Authors: | Ren Hong-Ping and Zhang Wu |
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| Affiliation: | School of Computer Engineering and Science, Shanghai University, Shanghai 200072, China; Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China |
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| Abstract: | The interpolating moving least-squares (IMLS) method is discussedfirst in this paper. And the formulae of the IMLS method obtained byLancaster are revised. Then on the basis of the boundaryelement-free method (BEFM), combining the boundary integral equation(BIE) method with the IMLS method, the improved boundaryelement-free method (IBEFM) for two-dimensional potential problemsis presented, and the corresponding formulae of the IBEFM areobtained. In the BEFM, boundary conditions are applied directly, butthe shape function in the MLS does not satisfy the property ofthe Kronecker δ function. This is a problem of the BEFM, andmust be solved theoretically. In the IMLS method, when the shape functionsatisfies the property of the Kronecker δ function, then theboundary conditions, in the meshless method based on the IMLSmethod, can be applied directly. Then the IBEFM, based on the IMLSmethod, is a direct meshless boundary integral equation method inwhich the basic unknown quantity is the real solution of the nodalvariables, and the boundary conditions can be applied directly andeasily, thus it gives a greater computational precision. Somenumerical examples are presented to demonstrate the method. |
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| Keywords: | moving least-squaresapproximation interpolating moving least-squares method meshless method improved boundary element-freemethod potential problem |
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